Finite Group Databasebeta

C22×#11763074 #17901699

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763074

Splittings

FittingC22×C17×#137 ⋊ C2
SylowC17 ⋊ C22×#471

Subgroups

subgroupG/H
centerC23#10587625
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#137C2
socleC23×C17#121
prime radicalC22×#10587635C2
hypercenterC22×#137D17
hypocenterC17C22×#471
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

2758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036943);